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Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 143))

Summary

Differential Evolution is currently one of the most popular heuristics to solve single-objective optimization problems in continuous search spaces. Due to this success, its use has been extended to other types of problems, such as multi-objective optimization. In this chapter, we present a survey of algorithms based on differential evolution which have been used to solve multi-objective optimization problems. Their main features are described and, based precisely on them, we propose a taxonomy of approaches. Some theoretical work found in the specialized literature is also provided. To conclude, based on our findings, we suggest some topics that we consider to be promising paths for future research in this area.

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References

  1. Abbass, H.A.: A Memetic Pareto Evolutionary Approach to Artificial Neural Networks. In: Stumptner, M., Corbett, D.R., Brooks, M. (eds.) Canadian AI 2001. LNCS (LNAI), vol. 2256, pp. 1–12. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Abbass, H.A.: The Self-Adaptive Pareto Differential Evolution Algorithm. In: Congress on Evolutionary Computation (CEC 2002), Piscataway, New Jersey, May 2002, vol. 1, pp. 831–836. IEEE Service Center (2002)

    Google Scholar 

  3. Abbass, H.A., Sarker, R.: The Pareto Differential Evolution Algorithm. International Journal on Artificial Intelligence Tools 11(4), 531–552 (2002)

    Article  Google Scholar 

  4. Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto-frontier Differential Evolution Approach for Multi-objective Optimization Problems. In: Proceedings of the Congress on Evolutionary Computation 2001 (CEC 2001), Piscataway, New Jersey, May 2001, vol. 2, pp. 971–978. IEEE Service Center (2001)

    Google Scholar 

  5. Babu, B.V., Jehan, M.M.L.: Differential Evolution for Multi-Objective Optimization. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Canberra, Australia, December 2003, vol. 4, pp. 2696–2703. IEEE Press, Los Alamitos (2003)

    Chapter  Google Scholar 

  6. Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)

    MATH  Google Scholar 

  7. Bean, J.C.: Genetics and random keys for sequencing and optimization. ORSA Journal on Computing 6(2), 154–160 (1994)

    MATH  Google Scholar 

  8. Chang, C.S., Xu, D.Y.: Differential Evolution Based Tuning of Fuzzy Automatic Train Operation for Mass Rapid Transit System. IEE Proceedings of Electric Power Applications 147(3), 206–212 (2000)

    Article  Google Scholar 

  9. Chang, C.S., Xu, D.Y., Quek, H.B.: Pareto-optimal set based multiobjective tuning of fuzzy automatic train operation for mass transit system. IEE Proceedings on Electric Power Applications 146(5), 577–583 (1999)

    Article  Google Scholar 

  10. Coello, C.A.C., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)

    MATH  Google Scholar 

  11. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)

    MATH  Google Scholar 

  12. Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Deb, K., Goldberg, D.E.: An Investigation of Niche and Species Formation in Genetic Function Optimization. In: David Schaffer, J. (ed.) Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, California, June 1989, pp. 42–50. George Mason University, Morgan Kaufmann Publishers (1989)

    Google Scholar 

  14. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  15. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multiobjective Optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. Theoretical Advances and Applications, pp. 105–145. Springer, USA (2005)

    Chapter  Google Scholar 

  16. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Reading (1989)

    MATH  Google Scholar 

  17. Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms, pp. 41–49. Lawrence Erlbaum Associates, Mahwah (1987)

    Google Scholar 

  18. Haimes, Y.Y., Lasdon, L.S., Wismer, D.A.: On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization. IEEE Transactions on Systems, Man, and Cybernetics 1(3), 296–297 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  19. Hanne, T.: On the convergence of multiobjective evolutionary algorithms. European Journal of Operational Research 117(3), 553–564 (1999)

    Article  MATH  Google Scholar 

  20. Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello, C.C., Caballero, R., Molina, J.: A New Proposal for Multi-Objective Optimization using Differential Evolution and Rough Sets Theory. In: Keijzer, M., et al. (eds.) 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), Seattle, Washington, USA, July 2006, vol. 1, pp. 675–682. ACM Press, New York (2006)

    Chapter  Google Scholar 

  21. Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello, C.A.C., Molina, J.: Pareto-adaptive ε-dominance. Evolutionary Computation 15(4), 493–517 (2007)

    Article  Google Scholar 

  22. Horn, J., Nafpliotis, N., Goldberg, D.E.: A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, Piscataway, New Jersey, June 1994, vol. 1, pp. 82–87. IEEE Service Center (1994)

    Google Scholar 

  23. Huband, S., Barone, L., While, L., Hingston, P.: A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005)

    Google Scholar 

  24. Huband, S., Hingston, P., Barone, L., While, L.: A Review of Multiobjective Test Problems and a Scalable Test Problem Toolkit. IEEE Transactions on Evolutionary Computation 10(5), 477–506 (2006)

    Article  Google Scholar 

  25. Iorio, A.W., Li, X.: Solving rotated multi-objective optimization problems using differential evolution. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 861–872. Springer, Heidelberg (2004)

    Google Scholar 

  26. Iorio, A.W., Li, X.: Incorporating Directional Information within a Differential Evolution Algorithm for Multi-objective Optimization. In: Keijzer, M., et al. (eds.) 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), Seattle, Washington, USA, July 2006, vol. 1, pp. 691–697. ACM Press, New York (2006)

    Chapter  Google Scholar 

  27. Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco, California (2001)

    Google Scholar 

  28. Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)

    Article  Google Scholar 

  29. Kukkonen, S., Lampinen, J.: An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 752–761. Springer, Heidelberg (2004)

    Google Scholar 

  30. Kukkonen, S., Lampinen, J.: GDE3: The third Evolution Step of Generalized Differential Evolution. In: 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, Scotland, September 2005, vol. 1, pp. 443–450. IEEE Service Center (2005)

    Google Scholar 

  31. Kursawe, F.: A Variant of Evolution Strategies for Vector Optimization. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 193–197. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  32. Lampinen, J.: De’s selection rule for multiobjective optimization. Technical report, Lappeenranta University of Technology, Department of Information Technology (2001)

    Google Scholar 

  33. Becerra, R.L., Coello, C.A.C.: Cultured differential evolution for constrained optimization. Computer Methods in Applied Mechanics and Engineering 195(33-36), 4303–4322 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Becerra, R.L., Coello, C.A.C.: Solving Hard Multiobjective Optimization Problems Using ε-Constraint with Cultured Differential Evolution. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 543–552. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  35. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multi-objective Optimization. Evolutionary Computation 10(3), 263–282 (2002)

    Article  Google Scholar 

  36. Li, H., Zhang, Q.: A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 583–592. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  37. Madavan, N.K.: Multiobjective Optimization Using a Pareto Differential Evolution Approach. In: Congress on Evolutionary Computation (CEC 2002), Piscataway, New Jersey, May 2002, vol. 2, pp. 1145–1150. IEEE Service Center (2002)

    Google Scholar 

  38. Mezura-Montes, E., Coello, C.A.C.: A Simple Multimembered Evolution Strategy to Solve Constrained Optimization Problems. IEEE Transactions on Evolutionary Computation 9(1), 1–17 (2005)

    Article  Google Scholar 

  39. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  40. Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI repository of machine learning databases (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html

  41. Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On Test Functions for Evolutionary Multi-objective Optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)

    Google Scholar 

  42. Parsopoulos, K.E., Taoulis, D.K., Pavlidis, N.G., Plagianakos, V.P., Vrahatis, M.N.: Vector Evaluated Differential Evolution for Multiobjective Optimization. In: 2004 Congress on Evolutionary Computation (CEC 2004), Portland, Oregon, USA, June 2004, vol. 1, pp. 204–211. IEEE Service Center (2004)

    Google Scholar 

  43. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(1), 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  44. Portilla Flores, E.A.: Integración Simultánea de Aspectos Estructurales y Dinámicos para el Diseño Óptimo de un Sistema de Transmisión de Variación Continua. PhD thesis, Departamento de Ingeniería Eléctrica, Sección de Mecatrónica, CINVESTAV-IPN, México, D.F., México (June 2006) (in Spanish)

    Google Scholar 

  45. Price, K.V.: An Introduction to Differential Evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill, London (1999)

    Google Scholar 

  46. Ranji Ranjithan, S., Kishan Chetan, S., Dakshima, H.K.: Constraint Method-Based Evolutionary Algorithm (CMEA) for Multiobjective Optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 299–313. Springer, Heidelberg (2001)

    Google Scholar 

  47. Reyes-Sierra, M., Coello, C.A.C.: Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art. International Journal of Computational Intelligence Research 2(3), 287–308 (2006)

    MathSciNet  Google Scholar 

  48. Robič, T., Filipič, B.: DEMO: Differential Evolution for Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)

    Google Scholar 

  49. Rudolph, G.: Some Theoretical Properties of Evolutionary Algorithms under Partially Ordered Fitness Values. In: Fabian, Cs., Intorsureanu, I. (eds.) Proceedings of the Evolutionary Algorithms Workshop (EAW 2001), Bucharest, Romania, January 2001, pp. 9–22 (2001)

    Google Scholar 

  50. Santana-Quintero, L.V., Coello, C.A.C.: An Algorithm Based on Differential Evolution for Multi-Objective Problems. International Journal of Computational Intelligence Research 1(2), 151–169 (2005)

    Article  MathSciNet  Google Scholar 

  51. Sarker, R., Abbass, H., Newton, C.: Solving Two Multi-objective Optimization Problems using Evolutionary Algorithm. In: Mohammadian, M., Sarker, R., Yao, X. (eds.) Computational Intelligence in Control. Idea Group Publishing, USA (2002)

    Google Scholar 

  52. David Schaffer, J.: Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, Hillsdale, New Jersey, pp. 93–100. Lawrence Erlbaum, Mahwah (1985)

    Google Scholar 

  53. Srigiriraju, K.C.: Noninferior Surface Tracing Evolutionary Algorithm (NSTEA) for Multi Objective Optimization. Master’s thesis, North Carolina State University, Raleigh, North Carolina (August 2000)

    Google Scholar 

  54. Srinivas, N., Deb, K.: Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 2(3), 221–248 (1994)

    Article  Google Scholar 

  55. Xue, F.: Multi-Objective Differential Evolution: Theory and Applications. PhD thesis, Rensselaer Polytechnic Institute, Troy, New York (September 2004)

    Google Scholar 

  56. Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based Multi-Objective Differential Evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Canberra, Australia, December 2003, vol. 2, pp. 862–869. IEEE Press, Los Alamitos (2003)

    Google Scholar 

  57. Xue, F., Sanderson, A.C., Graves, R.J.: Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm. In: 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, Scotland, September 2005, vol. 1, pp. 228–235. IEEE Service Center (2005)

    Google Scholar 

  58. Xue, F., Sanderson, A.C., Graves, R.J.: Multi-objective differential evolution - algorithm, convergence analysis, and applications. In: 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, Scotland, September 2005, vol. 1, pp. 743–750. IEEE Service Center (2005)

    Google Scholar 

  59. Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)

    Article  Google Scholar 

  60. Zitzler, E., Teich, J., Bhattacharyya, S.S.: Evolutionary Algorithm Based Exploration of Software Schedules for Digital Signal Processors. In: Banzhaf, W., Daida, J., Eiben, A.E., Garzon, M.H., Honavar, V., Jakiela, M., Smith, R.E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), July 1999, vol. 2, pp. 1762–1769. Morgan Kaufmann, San Francisco (1999)

    Google Scholar 

  61. Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)

    Article  Google Scholar 

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Uday K. Chakraborty

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Mezura-Montes, E., Reyes-Sierra, M., Coello, C.A.C. (2008). Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art. In: Chakraborty, U.K. (eds) Advances in Differential Evolution. Studies in Computational Intelligence, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68830-3_7

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  • DOI: https://doi.org/10.1007/978-3-540-68830-3_7

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